Three-dimensional space network key area identification method and device based on graph neural network

Abstract

The application discloses a three-dimensional space network key area identification method and device based on a graph neural network, and belongs to the technical field of network analysis. The method comprises the following steps: constructing a UAV communication network based on the distribution of UAVs in a three-dimensional space; dividing the UAV communication network into a plurality of non-overlapping areas to obtain an area graph; obtaining an initial feature representation of an area node based on the information of a basic node corresponding to the area node; performing layer neighborhood aggregation and representation updating operations on the area graph based on the initial feature representation to obtain an aggregated feature representation of the area node; and inputting the aggregated feature representation into a prediction module for prediction to obtain a prediction score of each area. The embodiment of the application can effectively identify key areas which have a significant influence on network connectivity.

Description

[0001] Technology Neighborhood This invention belongs to the field of network analysis technology, specifically relating to a method and apparatus for identifying key regions of a three-dimensional spatial network based on graph neural networks. Background Technology

[0002] Complex networks are frequently used to describe entities and their interactions in real-world systems, finding wide application in scenarios such as transportation, communication, infrastructure operation, energy supply, and unmanned system collaboration. A significant portion of these networks are not simply topological structures; their nodes and edges are embedded in specific physical spaces. Node locations, spatial distances, and local distribution all influence the network's connectivity and functional performance. For example, stations and roads in transportation systems have definite geographical locations; equipment deployment and signal transmission in communication are constrained by spatial distances; and platform nodes and interaction links in unmanned system collaboration exhibit different connectivity characteristics depending on their location. These types of networks can typically be modeled as spatial networks.

[0003] In networks with spatial embedding characteristics, real-world disturbances, protective measures, and resource allocation typically target local areas within a certain spatial range. Therefore, for spatial networks, critical components do not necessarily correspond to a single node or edge; multiple network elements within a local spatial range may collectively influence the network's connectivity and functional state. To identify the criticality of spatial network regions, existing technologies typically employ a two-dimensional spatial partitioning approach combined with regional index aggregation, evaluating regional importance based on the network disintegration effect after region removal. These methods offer strong interpretability and can intuitively reflect the structural attributes of nodes or edges within a region.

[0004] However, existing technologies for calculating region scores typically rely on manually designed centrality metrics, which struggle to adaptively characterize the nonlinear coupling relationships between spatial location, topological connectivity, and region adjacency. Furthermore, in scenarios where nodes exhibit a clear three-dimensional spatial distribution, two-dimensional region partitioning fails to fully represent their spatial structural characteristics. For these reasons, existing technologies suffer from poor accuracy in identifying key regions of three-dimensional spatial networks. Summary of the Invention

[0005] The technical problem to be solved by the present invention is that the above-mentioned methods commonly used in the prior art have poor accuracy when identifying key regions of three-dimensional spatial networks. In order to solve the above problem, the present invention provides a method and device for identifying key regions of three-dimensional spatial networks based on graph neural networks.

[0006] The content of this invention includes: In a first aspect, embodiments of the present invention provide a method for identifying key regions of a three-dimensional spatial network based on a graph neural network, comprising: A drone communication network is constructed based on the distribution of drones in three-dimensional space. The drone communication network is a three-dimensional spatial network. The basic nodes in the drone communication network are used to represent the drones, and the edges between the basic nodes are used to represent the communication links between drones. The UAV communication network is divided into multiple non-overlapping regions to obtain a region map. Each region is used to represent a cube structure in the UAV communication network. The region nodes in the region map are used to represent the region, and the edges between the region nodes are used to represent the connection relationship between the regions. The initial feature representation of the region node is obtained based on the information of the base node corresponding to the region node; Based on the initial feature representation, the operation is performed on the region map. The layer neighborhood aggregation and representation update operations are used to obtain the aggregated feature representation of the region nodes; The aggregated feature representation is input into the prediction module for prediction to obtain a prediction score for each region. The prediction score is used to characterize the importance of the region in the UAV communication network.

[0007] Optionally, dividing the UAV communication network into multiple non-overlapping regions to obtain a region map includes: The original three-dimensional coordinate values ​​of the basic node in the three-dimensional space are standardized to obtain normalized coordinate values. Based on the normalized coordinate values, the UAV communication network is divided into multiple non-overlapping cubic regions to obtain the region map.

[0008] Optionally, the connection relationship includes at least one of spatial adjacency relationship and entity interaction relationship. The spatial adjacency relationship is used to characterize that the cube structures corresponding to the two regions share a face, edge or vertex. The entity interaction relationship is used to characterize that there is an edge connection between the basic nodes contained in the two regions.

[0009] Optionally, obtaining the initial feature representation of the region node based on the information of the base node corresponding to the region node includes: The initial feature representation of the regional nodes is determined based on at least one of the regional degree centrality, regional webpage ranking, and regional collective influence. Wherein, the regional degree centrality is used to characterize the cumulative level of direct connectivity of the basic nodes contained in the region, the regional webpage ranking is used to characterize the relative importance of the basic nodes contained in the region in the overall connectivity of the UAV communication network, and the regional collective influence is used to characterize the degree of influence of the basic nodes contained in the region on the connectivity skeleton of the UAV communication network within a preset range.

[0010] Optionally, any region node in the region map Regional Degree Centrality Regional webpage sorting and regional collective influence They are respectively: ; ; ; in, Basic Node Degree centrality, Basic Node The degree, Let be the number of edges in the drone communication network. Basic Node PageRank value, Basic Node In radius The collective influence value. Optionally, the step of performing the initial feature representation on the region map is performed. The layer neighborhood aggregation and representation update operation yields the aggregated feature representation of the region nodes, including: The region map is input map sampling and aggregation encoder, and then executed. The layer neighborhood aggregation and representation update operations yield the aggregated feature representation of the region nodes. It is a positive integer; Among them, the Layer neighborhood aggregation and representation update operations include: The neighboring nodes of the target node are in the th order. The feature representations of the layers are aggregated to obtain the target node at the 1st layer. The neighborhood aggregation representation of the layer indicates that the target node is any of the region nodes, and the neighbor nodes are the region nodes in the region graph that are connected to the target node. ; The target node is in the first The feature representation of the layer and the target node in the th layer After concatenating the neighborhood aggregation representations of the layers, the target node at the 1st rank is obtained through linear transformation and nonlinear activation function. The feature representation of the layer, the target node in the th layer The feature representation of a layer is the aggregated feature representation of the target node, and the feature representation of the target node in layer 0 is the initial feature representation of the target node.

[0011] Optionally, after inputting the aggregated feature representation into the prediction module for prediction to obtain a prediction score for each region, the method further includes: A resource allocation strategy is formulated based on the predicted score of each of the regions. Based on the resource allocation strategy, communication resources are allocated to each of the regions.

[0012] Secondly, embodiments of the present invention also provide a device for identifying key regions of a three-dimensional spatial network based on a graph neural network, comprising: A construction module is used to construct a UAV communication network based on the distribution of UAVs in three-dimensional space. The UAV communication network is a three-dimensional spatial network. The basic nodes in the UAV communication network are used to represent the UAVs, and the edges between the basic nodes are used to represent the communication links between the UAVs. The partitioning module is used to divide the UAV communication network into multiple non-overlapping regions to obtain a region map. Each region is used to represent a cube structure in the UAV communication network. The region nodes in the region map are used to represent the regions, and the edges between the region nodes are used to represent the connection relationships between the regions. The acquisition module is used to acquire the initial feature representation of the region node based on the information of the base node corresponding to the region node; An execution module is configured to perform operations on the region map based on the initial feature representation. The layer neighborhood aggregation and representation update operations are used to obtain the aggregated feature representation of the region nodes; The prediction module is used to input the aggregated feature representation into the prediction module for prediction, and obtain a prediction score for each region. The prediction score is used to characterize the importance of the region in the UAV communication network.

[0013] Thirdly, embodiments of the present invention provide an electronic device, including: a memory, a processor, and a program stored in the memory and executable on the processor; the processor is configured to read the program in the memory to implement the steps in the method for identifying key regions of a three-dimensional spatial network based on a graph neural network as described in the first aspect.

[0014] Fourthly, embodiments of the present invention provide a readable storage medium for storing a program, which, when executed by a processor, implements the steps in the method for identifying key regions of a three-dimensional spatial network based on a graph neural network as described in the first aspect.

[0015] The beneficial effects of this invention are that, in its embodiments, dividing the UAV communication network into non-overlapping cubic regions and constructing a region map allows for the identification of key components within the UAV communication network at the regional scale, which is more conducive to supporting tasks such as network protection, resilience enhancement, propagation intervention, and resource allocation. Simultaneously, by obtaining initial regional features based on basic node information and performing multi-layer neighborhood aggregation on the region map, local and global topology information can be efficiently fused, accurately capturing spatial dependencies between regions. Finally, through the region prediction scores output by the prediction module, key regions in the network can be automatically and quantitatively identified, avoiding reliance on human experience and improving the accuracy and robustness of identification, thus providing reliable support for resource optimization and topology management of the UAV communication network. Attached Figure Description

[0016] Figure 1 A flowchart illustrating the method for identifying key regions of a three-dimensional spatial network based on a graph neural network, as provided in an embodiment of the present invention. Figure 2a This is a schematic diagram of a drone communication network. Figure 2b The result of region division in three-dimensional space; Figure 2c A schematic diagram showing the joint representation of the UAV communication network and the region division results; Figure 2d This is a schematic diagram of a region map constructed from a drone communication network. Figure 3 This is a schematic diagram illustrating the process of generating a region map; Figure 4 This is a schematic diagram of a graph learning process based on a region map. Figure 5 A schematic diagram of the regional key ranking sequence; Figure 6 A schematic diagram of a key region identification device for three-dimensional spatial networks based on graph neural networks provided in this embodiment of the invention; Figure 7 This is a schematic diagram of the structure of an electronic device provided in an embodiment of the present invention. Detailed Implementation

[0017] In the embodiments of this application, the term "and / or" describes the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, and B existing alone. The character " / " generally indicates that the preceding and following related objects have an "or" relationship. In the embodiments of this application, the term "multiple" refers to two or more, and other quantifiers are similar. The terms "first," "second," etc., in the specification of this application are used to distinguish similar objects and are not used to describe a specific order or sequence. It should be understood that such terms can be interchanged where appropriate so that embodiments of this application can be implemented in orders other than those illustrated or described herein, and the objects distinguished by "first" and "second" are usually of the same class, without limiting the number of objects. For example, the first object can be one or multiple.

[0018] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of the embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0019] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art relating to this application. The terminology used herein is for the purpose of describing embodiments of this application only and is not intended to be limiting of this application.

[0020] First, let's analyze some of the terms used in this application: The following explains the relevant content of complex networks. Complex networks are typically used to abstractly describe the entities in a system and their interactions. Unlike ordinary networks that only focus on topological relationships, spatial networks also need to describe the location attributes of nodes in geographic or embedded space. Spatial network disintegration is usually examined by removing nodes, edges, or specific regions from the network, to observe the degradation process of network functionality and structural characteristics. The more significant the network performance degradation caused by region removal, the more critical the role that region plays in maintaining the overall operation and structural stability of the network, and the higher its importance. The two-dimensional space in which the network resides is divided into... Let the set of regions be _ . , Indicates the first A region. Given a region removal sequence. .in, For a set of region indexes A permutation. According to the sequence. When removing regions step by step, the remaining network after removal can be denoted as: .in, This represents the set of invalid nodes that were removed from the first k regions. This represents the set of edges that are invalidated due to their association with the removed node.

[0021] To measure network performance after region removal, the Largest Connected Component (LCC) metric is introduced. Let the network... The set of connected components is Then its maximum connected component size is To eliminate the impact of differences in network size on the evaluation results, a normalized maximum connected component ratio is further defined. : ; in, The smaller the value, the lower the proportion of the largest connected component in the network, the more the overall network connectivity is disrupted, and the lower the performance.

[0022] During continuous region removal, based on the region removal ratio The horizontal axis represents changes in network connectivity. To measure the overall disintegration effect of the region removal strategy, the area under the LCC curve (AUC) can be used as an evaluation metric; the smaller the AUC, the better the overall disintegration effect of the removal sequence. Since... The horizontal axis interval between two adjacent sampling points is Therefore, the discrete AUC can be expressed as: ; The following section explains the relevant content of Graph Neural Networks (GNNs). GNNs are a type of representation learning method for graph-structured data. They are suitable for processing non-Euclidean structured data composed of nodes, edges, and node features. The basic idea is to gradually update node representations through information transfer between nodes and neighborhood aggregation, so that node embeddings can simultaneously contain their own attributes and neighborhood structure information.

[0023] Generally, the computation process of a GNN can be summarized into four stages: feature initialization, neighborhood aggregation, representation update, and task output. In the feature initialization stage, the original attributes of the node are used as the initial node representation. For each node... Let its initial eigenvector be Then the node at level 0 represents It can be recorded as: ; In the neighborhood aggregation stage, the GNN collects information about the target node's neighborhood based on adjacency relationships in the graph and aggregates the previous layer representations of neighboring nodes. Graph Sampling and Aggregate (GraphSAGE), a typical spatial domain graph neural network model, focuses on sampling and aggregating the neighboring nodes of the target node to generate node embedding representations. Typically, this is done in the first... In the layer, set nodes In the The layer is represented as Its neighbor set is GraphSAGE first started from... Sample several neighboring nodes and aggregate the upper-level representations of these neighboring nodes to obtain the node. In the Neighborhood aggregation representation of layers : ; in, The neighborhood aggregation function can take the form of mean aggregation, pooling aggregation, or Long Short-Term Memory (LSTM) aggregation.

[0024] During the representation update phase, after obtaining the neighborhood representation, GraphSAGE concatenates the target node's previous-layer representation with the neighborhood representation, and then obtains a new node representation through linear transformation and a non-linear activation function. Specifically, the node... In the Layer representation for: ; in,[· ·] indicates vector concatenation. For the first The learnable parameter matrix of the layer, It is a non-linear activation function. Through multi-level sampling and aggregation, the node representation can gradually integrate its own attributes and structural information within a multi-hop neighborhood.

[0025] During the task output phase, the process will be... Node representation after layer update Input the data into the downstream task module to obtain the corresponding prediction results.

[0026] Based on this, the embodiments of this application provide a method and apparatus for identifying key regions of a three-dimensional spatial network based on graph neural networks, aiming to characterize the structural features of the spatial network from a regional perspective, introduce GNN to carry out graph representation learning, mine regional attributes and inter-regional relationships, and realize the evaluation and ranking of the importance of key regions.

[0027] Please see Figure 1 , Figure 1 This is a flowchart illustrating the method for identifying key regions of a 3D spatial network based on a graph neural network according to an embodiment of the present invention. The method specifically includes the following steps: Step 101: Construct a UAV communication network based on the distribution of UAVs in three-dimensional space. The UAV communication network is a three-dimensional spatial network. The basic nodes in the UAV communication network are used to represent the UAVs, and the edges between the basic nodes are used to represent the communication links between the UAVs.

[0028] Step 102: Divide the UAV communication network into multiple non-overlapping regions to obtain a region map. Each region is used to represent a cube structure in the UAV communication network. Region nodes in the region map are used to represent the region, and edges between the region nodes are used to represent the connection relationship between the regions.

[0029] Step 103: Obtain the initial feature representation of the region node based on the information of the base node corresponding to the region node.

[0030] Step 104: Perform on the region map based on the initial feature representation. The layer neighborhood aggregation and representation update operations are used to obtain the aggregated feature representation of the region nodes.

[0031] Step 105: Input the aggregated feature representation into the prediction module for prediction to obtain a prediction score for each region. The prediction score is used to characterize the importance of the region in the UAV communication network.

[0032] The spatial embedded communication network constructed based on the distribution of UAVs in three-dimensional space constitutes the UAV communication network in this embodiment. This UAV communication network is a three-dimensional spatial network, and the position of each UAV is determined by three-dimensional coordinates. The UAV communication network is denoted as... , Represents the set of basic nodes. This represents the set of edges. For ease of description, the current 3D spatial domain is referred to as the original spatial domain. By constructing a 3D coordinate system in the original spatial domain, the original 3D coordinate values ​​of the basic nodes can be obtained. In some embodiments, the UAV communication network is divided into multiple non-overlapping cubic regions in the original spatial domain to obtain a region map.

[0033] In different UAV spatial embedded communication network instances, the spatial distribution range, coordinate scale, and deployment density of UAVs may vary. Directly dividing the region based on the original 3D coordinate values ​​can easily lead to the model input being overly sensitive to specific spatial scales, which is not conducive to unified modeling across different instances.

[0034] Optionally, in some embodiments, step 102 includes: The original three-dimensional coordinate values ​​of the basic node in the three-dimensional space are standardized to obtain normalized coordinate values. Based on the normalized coordinate values, the UAV communication network is divided into multiple non-overlapping cubic regions to obtain the region map.

[0035] First, the original three-dimensional coordinate values ​​of the basic nodes in the UAV communication network are standardized. For any basic node... Set basic nodes The original three-dimensional coordinates are ,in, Represents the basic node In the Coordinate values ​​in each dimension For the base node In the Original three-dimensional coordinates in each dimension Its normalized form for: ; in, This represents the total number of basic nodes in the drone communication network. Basic Node In the Coordinates in each dimension Used to characterize the minimum value function Used to characterize the maximum value function. It should be noted that in the actual calculation process, if all node coordinates of a certain dimension are the same, the normalized value of that dimension can be uniformly set to 0 to avoid the denominator being 0.

[0036] Through the above standardization process, the three-dimensional spatial network is projected from the original spatial domain to a three-dimensional standard spatial domain, thereby eliminating the differences in spatial scale and distribution range under different UAV deployment scenarios and making the network model scale invariant. At the same time, this process maps the coordinates to a standard interval, providing a unified calculation benchmark for subsequent region partitioning based on regular cubic meshes, ensuring the consistency and reproducibility of the region partitioning strategy under different scenarios, and thus improving the model's generalization ability and robustness to diverse deployment environments.

[0037] After standardizing the original 3D coordinates of all basic nodes, the UAV communication network is divided into cubic regions within a 3D standard spatial domain. In some embodiments, the UAV communication network is divided into multiple non-overlapping cubic regions of the same size according to a preset cube. In other embodiments, the UAV communication network is divided into multiple non-overlapping regions according to the number of basic nodes, with each region containing the same number of basic nodes.

[0038] As a specific example, the three-dimensional standard spatial domain Divide the regular cube into its components. A set of non-overlapping cubic regions, denoted as: ; in, Indicates the first A cube-shaped region Indicates the area The above method ensures the consistency of spatial scale among different regions, avoiding feature extraction bias caused by uneven region size.

[0039] In practical implementation, nodes located on the boundary of a region can be uniquely assigned to a certain region according to a preset boundary assignment rule. The specific preset boundary assignment rule is not limited here, as long as the uniqueness of the mapping between the basic node and the region can be guaranteed.

[0040] area The set of basic nodes contained in it can be represented as: After establishing the mapping between base nodes and region nodes, a region graph is constructed. ,in, Represents the set of basic nodes in the region. This represents the set of edges between nodes in a region graph. Each region node in the region graph corresponds to a region, and each connecting edge reflects the multiple coupling mechanisms between regions.

[0041] In specific implementation, the existence of edges between regions is determined based on pre-set connection rules. Optionally, in some embodiments, the connection relationship includes at least one of spatial adjacency and entity interaction, wherein the spatial adjacency is used to characterize that the cube structures corresponding to the two regions share a face, edge, or vertex, and the entity interaction is used to characterize that there is an edge connection between the basic nodes contained in the two regions.

[0042] In some embodiments, the existence of a connection between any two regions is determined based on spatial adjacency. If the cube structures corresponding to the two regions share a face, edge, or vertex, then the two regions are considered to have a spatial adjacency relationship. In the region graph, the nodes of these two regions are connected by an edge.

[0043] In other embodiments, the existence of an edge between any two regions is determined based on the cross-regional entity interaction relationship. If there is an edge connection between basic nodes belonging to different regions in the UAV communication network, then an edge is established between the corresponding regional nodes. In this embodiment, the regional coupling structure induced by the interaction of UAV communication network can be characterized by the cross-regional entity interaction relationship.

[0044] As a specific implementation, after dividing the UAV communication network into multiple regions, it is sequentially determined whether there is a spatial adjacency relationship and / or a physical interaction relationship between any two regions. If at least one of a spatial adjacency relationship and a physical interaction relationship exists between two regions, an edge is set between the nodes of the two regions to obtain the final region graph. Through the above method, the original UAV communication network... Converted into a region map While preserving spatial organization information and inter-regional relationship structure, it provides structured input for subsequent graph neural network modeling.

[0045] As a specific example, please refer to Figure 2a The drones are distributed in three-dimensional space, forming a spatially embedded drone communication network for collaborative perception, information exchange, and distributed control. Each node in the drone communication network represents a drone, and the edges between nodes represent communication links between drones. In this embodiment, the drones are distributed in three-dimensional space, and their topology is determined by both spatial location and communication constraints. Figure 2b This demonstrates the results of region division in three-dimensional space. For example... Figure 2b As shown, the entire space is uniformly divided into several cubic units of equal size, with each cube corresponding to a region, used to characterize the local spatial structure features. Figure 2c A schematic diagram showing the joint representation of the UAV communication network and the region division results. Figure 2c In this model, cubic regions are superimposed on the original UAV distribution as spatial analysis units. It should be understood that in the actual implementation, some regions may not contain UAVs, while regions containing UAVs are used for further structural modeling. Different colors are used to distinguish different spatial regions to reflect the spatial heterogeneity of the region divisions. Figure 2dThis is a schematic diagram of a region graph constructed from a drone communication network. Each non-empty cube region is mapped to a region node in the region graph, and the edge relationships between region nodes are generated based on the communication relationships between drones within the region. For example, when there is a communication connection between drones in two different regions, an edge is established between the corresponding region nodes, thereby forming a region-level spatial network representation.

[0046] Region features are used to characterize the structural role of regions in UAV communication networks and their potential impact on network connectivity, serving as important inputs for subsequent graph neural network learning of region representations. It is important to consider that the criticality of a region depends not only on the scale of connections within or between regions, but also on its propagation role in global connectivity relationships and its collective influence within multi-hop neighborhoods.

[0047] In some embodiments, at least one of the following metrics is selected to constitute the initial feature representation of a region: Regional Degree Centrality (RDC), Regional PageRank (RPR), Regional Collective Influence (RCI), Regional Average Degree, Number of Edges in the Region, and Regional Eigenvector Centrality. The Regional Average Degree measures the importance of the region by the arithmetic mean of the degree of nodes within the region. The Number of Edges in the Region measures the importance of the region by counting the number of edges that intersect with the cube region. The Regional Eigenvector Centrality measures the importance of the region in the global structure by summing the eigenvector centrality values ​​of each node within the cube region.

[0048] Optionally, in some embodiments, step 103 includes: The initial feature representation of the nodes in the region is determined based on at least one of the region degree centrality, region PageRank, and region collective influence. Wherein, the regional degree centrality is used to characterize the cumulative level of direct connectivity of the basic nodes contained in the region, the regional PageRank is used to characterize the relative importance of the basic nodes contained in the region in the overall connectivity of the UAV communication network, and the regional collective influence is used to characterize the degree of influence of the basic nodes contained in the region on the connectivity skeleton of the UAV communication network within a preset range.

[0049] Regional degree centrality is used to characterize the cumulative level of direct connectivity among basic nodes within a region. A higher regional degree centrality indicates stronger direct connectivity among the basic nodes within that region, potentially having a greater impact on the local connectivity structure of the UAV communication network. For any regional node... Its internal set of basic nodes is Set the basic node. In the original drone communication network The degree in The total number of nodes in the drone communication network is Specifically, regional nodes Regional Degree Centrality for: ; in, Basic Node Degree centrality, Basic Node The degree, Let be the number of edges in the drone communication network.

[0050] Regional PageRank is used to characterize the global influence of basic nodes within a region from the perspective of importance propagation. This metric reflects the relative importance of basic nodes within a region in the overall connectivity of the UAV communication network. If a region contains multiple basic nodes with high PageRank, it indicates that the region may be in a relatively important position in the network's connection or influence propagation. Specifically, regional nodes... Regional PageRank for: ; in, Basic Node PageRank value.

[0051] Regional collective influence is used to characterize the potential impact of basic nodes within a region on the network connectivity framework within a certain range. A larger regional collective influence indicates that the basic nodes within that region may have a stronger ability to disrupt connectivity structures within a larger neighborhood. Regional nodes Regional collective influence for: ; in, Basic Node In radius The collective influence value.

[0052] As a specific implementation, the initial feature representation of the region node is determined based on the above three types of region centrality features, wherein the region node The initial feature representation is defined as For empty regions that do not contain basic nodes, their corresponding eigenvalues ​​are uniformly set to 0. By organizing the initial feature representations of all region nodes, the region feature matrix can be obtained. ,in, The transpose symbol is used. Region feature matrix. With the set of region edges Together constituting a region map Input information.

[0053] In this embodiment, based on the initial feature representation of the region nodes, a graph convolutional network is used to perform information transfer and neighborhood aggregation between region nodes on the region graph.

[0054] Optionally, in some embodiments, step 104 includes: The region map is input map sampling and aggregation encoder, and then executed. The layer neighborhood aggregation and representation update operations yield the aggregated feature representation of the region nodes. It is a positive integer; Among them, the Layer neighborhood aggregation and representation update operations include: The neighboring nodes of the target node are in the th order. The feature representations of the layers are aggregated to obtain the target node at the 1st layer. The neighborhood aggregation representation of the layer indicates that the target node is any of the region nodes, and the neighbor nodes are the region nodes in the region graph that are connected to the target node. ; The target node is in the first The feature representation of the layer and the target node in the th layer After concatenating the neighborhood aggregation representations of the layers, the target node at the 1st rank is obtained through linear transformation and nonlinear activation function. The feature representation of the layer, the target node in the th layer The feature representation of a layer is the aggregated feature representation of the target node, and the feature representation of the target node in layer 0 is the initial feature representation of the target node.

[0055] Set up regional nodes The set of neighbor nodes in the region graph for: ; Based on the initial feature representation of the region nodes, perform on the region graph The layer neighborhood aggregation and representation update operations yield the aggregated feature representation of the region nodes. Specifically, in the first layer... During the layer neighborhood aggregation and representation update operations, the region is first processed. The feature representations of the neighboring nodes are aggregated to obtain the neighborhood aggregate representation. : ; ; in, Indicates the first The neighborhood aggregation function of the layer can take forms such as mean aggregation and pooling aggregation. This process can aggregate the structural and feature information of the neighborhood region into the representation of the target region. Furthermore, the region nodes... The upper layer of itself represents Aggregation with Neighborhood By merging, regional nodes are obtained. No. Layer feature representation : ; in, For regional nodes In the Layer feature representation, This represents vector concatenation. For the first The weight matrix of the layer, It is a non-linear activation function. After multiple layers of neighborhood aggregation and representation update operations, the embedded representation of each region node not only contains its own region features, but also incorporates the structural association information of neighboring regions.

[0056] go through After layer neighborhood aggregation and representation update operations, the aggregated feature representation of all region nodes can be summarized as follows: ; in, Represents the region aggregation embedding matrix. For regional nodes The aggregation feature representation, This represents the number of nodes in the region. Because multi-layer GraphSAGE can progressively expand the scope of region information aggregation, the final aggregated feature representation can reflect the combined influence of the region and its multi-hop neighborhood.

[0057] After obtaining the aggregated feature representations of the region nodes, these representations are input into the prediction module for prediction, yielding a prediction score for each region. It should be understood that the specific structure of the prediction module is not limited here. For example, in some embodiments, a multilayer perceptron is used as the prediction module to map the aggregated feature representations of the region nodes to the region's key prediction scores. For region nodes... Its predicted score Represented as: ; in, This represents the parameterized scoring function corresponding to the multilayer perceptron. A higher prediction score indicates greater importance of the region within the UAV communication network, and thus greater importance during network collapse. The prediction scores of all regions can be represented as a vector. : .

[0058] It should be understood that the embodiments of the present invention can be used to identify key areas of other three-dimensional spatial networks besides UAVs and communication networks, such as three-dimensional spatial transportation networks, base station communication networks, and infrastructure protection networks. In this embodiment, after identifying key components in the spatial network at the regional scale and determining the importance of the region based on the prediction score, tasks such as network protection, resilience enhancement, propagation intervention, and resource allocation can be achieved based on the prediction score. Optionally, in some embodiments, after step 105, the method further includes: A resource allocation strategy is formulated based on the predicted score of each of the regions. Based on the resource allocation strategy, communication resources are allocated to each of the regions.

[0059] In this embodiment, the importance of each region in the UAV communication network is identified and ranked on a regional basis. Based on the predicted scores of the regions, a resource allocation strategy is formulated to provide priority resource allocation and protection for UAV nodes in key regions. In this way, regions with higher predicted scores can obtain more communication resources, thereby improving the overall communication reliability and resilience of the network.

[0060] As can be seen from the foregoing, in some embodiments, the region removal ratio is used as the horizontal axis of the LCC curve, wherein, The smaller the value, the faster the generated regional criticality ranking sequence can reduce LCC with a smaller region removal ratio, resulting in a better overall disintegration effect. Therefore, AUC can be used as a core indicator for evaluating regional ranking quality and network disintegration capability. Optionally, in some embodiments, after step 105, the method further includes: The regions are sorted in descending order according to the predicted scores to obtain a region key ranking sequence; Regions are removed sequentially according to the region criticality sorting sequence, and the normalized maximum connected component ratio of the remaining network at each step is calculated. The AUC value of the regional criticality ranking sequence is calculated based on the normalized maximum connected component ratio. The validity of the regional key ranking sequence is determined based on the AUC value.

[0061] By sorting all regions in descending order based on their predicted scores, a region priority ranking sequence can be obtained. : ; The sorting results satisfy: ; Regions ranked higher receive higher prediction scores, indicating that the model considers these regions to provide stronger support for the network connectivity structure and should be prioritized for removal during region disintegration. Thus, the region scores output by the model are transformed into a complete sequence of region removals, providing a foundation for subsequent evaluation of disintegration effectiveness.

[0062] In some embodiments, after obtaining the regional key ranking sequence Then, regions are removed sequentially according to their regional criticality ranking, and the normalized maximum connected component ratio of the remaining network is calculated at each step. Let the sequence be... The remaining network obtained after removing the first k regions is Its normalized maximum connected component ratio Recorded as: ; in, This indicates the total number of regions.

[0063] In some embodiments, the region map is input to a GraphSAGE encoder and executed. The layer neighborhood aggregation and representation update operations yield the aggregated feature representation of the region nodes. In this embodiment, the GraphSAGE encoder and prediction module can be pre-trained using training samples. Let the parameter set in the GraphSAGE encoder and region scoring function be... The model training process can then be represented as: ; in, This represents the model parameters after training. This is the predicted score vector output by the model. This is the supervised label vector. During training, the samples are divided into a training set, a validation set, and a test set. The training set is used for updating model parameters, the validation set is used to monitor the training process and assist in model selection, and the test set is used to evaluate the model's generalization ability on unseen samples.

[0064] In some embodiments, it is first necessary to generate multiple three-dimensional spatial networks and their corresponding supervision labels as training sample data. The specific generation process of multiple three-dimensional spatial networks will not be described in detail here. The following mainly describes the generation process of supervision labels.

[0065] The criticality of a region is determined by its impact on the overall connectivity structure during network disintegration. Based on the aforementioned content regarding complex networks, the overall disintegration effect of a region removal sequence can be evaluated using AUC. For a set of regions... The goal is to obtain a region removal sequence that minimizes the corresponding AUC. Therefore, the region disintegration optimization objective can be expressed as: ; in, Represents a set of regions All possible permutations, This represents the optimal region removal sequence that minimizes the AUC. Since the number of possible permutations increases significantly with the number of regions, directly enumerating the optimal sequence becomes computationally difficult. Therefore, this embodiment employs a combination of region selection and local combinatorial search to construct an approximate monitoring signal.

[0066] Specifically, firstly, based on regional structural indicators or initial disintegration assessment results, select from all regions. Each region forms a region set. Subsequently, Enumerate from 1 to 1 respectively The algorithm identifies candidate removal combinations consisting of several regions and calculates the impact of removing different combinations on the LCC. This approach avoids enumerating all permutations while obtaining several candidate solutions with better disintegration effects. In practical implementation, and The value of can be determined through parameter sensitivity analysis, and no specific limit is specified here.

[0067] To obtain key regional monitoring signals, this embodiment first screens candidate solutions with better performance based on the disintegration effect of regional removal results, and then statistically analyzes the regional... The frequency of occurrence in excellent candidate solutions is denoted as . This frequency reflects the region. The degree of stable occurrence in high-quality disintegration schemes. If a certain region frequently appears in candidate schemes with good disintegration effects, it indicates that it makes a high contribution to reducing the maximum connectivity of the network.

[0068] However, when using only the frequency of region occurrence to construct labels, a few regions may obtain high label values ​​due to their frequent appearance in excellent candidate solutions, but a large number of regions may have the same frequency, especially regions with a frequency of 0. In this case, the label distribution is relatively sparse, and the model has difficulty further distinguishing the relative importance of these regions with the same frequency, which can easily lead to insufficient ranking information in the later part of the region removal sequence.

[0069] To enhance the stability of the monitoring signal, this embodiment further introduces a regional degree ratio as a lightweight correction term. Let... Indicates the area The degree ratio characteristics, then the region Unnormalized labels Defined as: ; in, This is a correction coefficient used to control the influence of the region degree ratio on the labels. To facilitate model training and reduce the impact of label scale differences between different network instances, the unnormalized labels for all regions are normalized: ; in, Indicates the area The final supervisory label, The larger the value, the greater the contribution of that region to a superior disintegration scheme, and the higher the critical prediction score should be assigned to it during model training. The supervision labels for all regions constitute the label vector. : ; The above method transforms the overall disintegration effect of the region removal sequence into a region-level supervision signal. This label reflects the frequency of the region's occurrence in a high-quality disintegration scheme, and the label sparsity problem is alleviated by degree ratio correction, providing a training target for the GraphSAGE model to learn the region key scores.

[0070] The prediction vector This will be combined with the supervision label vector constructed earlier. Alignment is used for subsequent model training and parameter optimization. After training, the model can be aligned accordingly. The regions are sorted to generate a key region removal sequence for the disintegration of 3D spatial networks.

[0071] During the training process, it is known that This is a region-specific key label vector. Let be the predicted score vector for a region. The training objective is to minimize the deviation between the predicted score and the supervision label within the parameter space. Considering that the key labels for regions are continuous values, this embodiment first uses weighted mean square error to characterize the numerical difference between the predicted score and the supervision label. Let the region... The supervisory label is The predicted score is Then the weighted mean square error It can be represented as: ; in, Indicates the area The corresponding loss weights. Relying solely on mean squared error can constrain the closeness between predicted and labeled values, but the region disintegration task focuses more on the relative priority between regions. Therefore, this embodiment further introduces ranking loss to enhance the model's ability to learn the ranking relationships of key regions. For a set of region pairs ,like Then the expected model prediction result satisfies The corresponding sorting loss. It can be represented as: ; in, This represents the set of regions that participate in the sorting constraints. This represents the sorting interval parameter. The total loss function of the model, combining numerical regression error and sorting constraints, is... Defined as: ; in, The balancing coefficient is used to adjust the relative contributions of the regression error term and the ranking constraint term to the overall training objective. By minimizing the above loss function, the model can simultaneously learn the numerical distribution of key region labels and their relative ranking relationships, thereby improving the performance of key region identification and region removal sequence generation.

[0072] As a specific example, please refer to Figures 3-5 First, three-dimensional (3D) spatial network training samples are generated. Then, the original node-level network is converted into a region-level representation by partitioning it into cubes (preferably cubic), resulting in a region-level representation. Finally, a region map is generated. Figure 3 A schematic diagram of the region graph generation process is provided. The region graph is then constructed based on the spatial adjacency and entity interaction relationships of the regions, and RDC, RPR, and RCI are extracted as region node features to obtain the initial feature vectors of the region nodes. Based on this, and according to the aforementioned content, supervision labels are constructed by combining the frequency of occurrence of regions in the optimal disintegration scheme with a degree ratio correction term; then, the GraphSAGE encoder is used to aggregate the features of the region graph. Specifically, the region graph containing the initial feature vectors is used as input, undergoes L layers of neighborhood aggregation and representation update operations, outputs the aggregated feature representation of the region nodes, and outputs the prediction score of the region through MLP. The higher the prediction score, the more important the region. Figure 4 A schematic diagram of the graph learning process based on region maps is presented. Finally, the importance of regions is determined based on the predicted scores, and the regions are ranked from highest to lowest importance to generate a region criticality ranking sequence. Regions are then removed sequentially according to this ranking sequence, and the overall disintegration effect of the sequence is evaluated using the LCC curve AUC. Figure 5 This is a schematic diagram of the regional key ranking sequence.

[0073] In this embodiment, a key region identification method combining cube region partitioning and graph neural network is provided. This method takes spatial regions rather than individual nodes as the analysis object, and by fusing network topology information and spatial distribution information, it mines regional attributes and inter-regional relationships to achieve importance assessment and ranking of key regions in three-dimensional spatial network.

[0074] like Figure 6 As shown, this embodiment of the invention also provides a 3D spatial network key region identification device 600 based on graph neural networks, comprising: The construction module 601 is used to construct a UAV communication network based on the distribution of UAVs in three-dimensional space. The UAV communication network is a three-dimensional space network. The basic nodes in the UAV communication network are used to represent the UAVs, and the edges between the basic nodes are used to represent the communication links between the UAVs. The partitioning module 602 is used to divide the UAV communication network into multiple non-overlapping regions to obtain a region map. Each region is used to represent a cube structure in the UAV communication network. The region nodes in the region map are used to represent the region, and the edges between the region nodes are used to represent the connection relationship between the regions. The acquisition module 603 is used to acquire the initial feature representation of the region node based on the information of the base node corresponding to the region node; Execution module 604 is configured to perform on the region map based on the initial feature representation. The layer neighborhood aggregation and representation update operations are used to obtain the aggregated feature representation of the region nodes; The prediction module 605 is used to input the aggregated feature representation into the prediction module for prediction to obtain a prediction score for each region, and the prediction score is used to characterize the importance of the region in the UAV communication network.

[0075] Optionally, the partitioning module 602 includes: The standardization processing unit is used to standardize the original three-dimensional coordinate values ​​of the basic node in the three-dimensional space to obtain normalized coordinate values. A partitioning unit is used to divide the UAV communication network into multiple non-overlapping cubic regions based on the normalized coordinate values, thereby obtaining the region map.

[0076] Optionally, the connection relationship includes at least one of spatial adjacency relationship and entity interaction relationship. The spatial adjacency relationship is used to characterize that the cube structures corresponding to the two regions share a face, edge or vertex. The entity interaction relationship is used to characterize that there is an edge connection between the basic nodes contained in the two regions.

[0077] Optionally, the acquisition module 503 is specifically used for: The initial feature representation of the regional nodes is determined based on at least one of the regional degree centrality, regional webpage ranking, and regional collective influence. Wherein, the regional degree centrality is used to characterize the cumulative level of direct connectivity of the basic nodes contained in the region, the regional webpage ranking is used to characterize the relative importance of the basic nodes contained in the region in the overall connectivity of the UAV communication network, and the regional collective influence is used to characterize the degree of influence of the basic nodes contained in the region on the connectivity skeleton of the UAV communication network within a preset range.

[0078] Optionally, any region node in the region map Regional Degree Centrality Regional webpage sorting and regional collective influence They are respectively: ; ; ; in, Basic Node Degree centrality, Basic Node The degree, Let be the number of edges in the drone communication network. Basic Node PageRank value, Basic Node In radius The collective influence value. Optionally, the execution module 604 is specifically used for: The region map is input map sampling and aggregation encoder, and then executed. The layer neighborhood aggregation and representation update operations yield the aggregated feature representation of the region nodes. It is a positive integer; Among them, the Layer neighborhood aggregation and representation update operations include: The neighboring nodes of the target node are in the th order. The feature representations of the layers are aggregated to obtain the target node at the 1st layer. The neighborhood aggregation representation of the layer indicates that the target node is any of the region nodes, and the neighbor nodes are the region nodes in the region graph that are connected to the target node. ; The target node is in the first The feature representation of the layer and the target node in the th layer After concatenating the neighborhood aggregation representations of the layers, the target node at the 1st rank is obtained through linear transformation and nonlinear activation function. The feature representation of the layer, the target node in the th layer The feature representation of a layer is the aggregated feature representation of the target node, and the feature representation of the target node in layer 0 is the initial feature representation of the target node.

[0079] Optionally, the graph neural network-based 3D spatial network key region identification device 600 further includes: A formulation module is used to formulate a resource allocation strategy based on the predicted score of each of the regions; The allocation module is used to allocate communication resources to each of the regions based on the resource allocation strategy.

[0080] The key region identification device 600 based on graph neural network in this embodiment can execute the above method embodiment. Its implementation principle and technical effect are similar, and will not be described again here.

[0081] It should be noted that the division of units in the embodiments of this application is illustrative and only represents one logical functional division. In actual implementation, other division methods may be used. Furthermore, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated units described above can be implemented in hardware or as software functional units.

[0082] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a processor-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) or processor to execute all or part of the steps of the methods described in the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0083] like Figure 7As shown, this application provides an electronic device 700, including: a memory 702, a processor 701, and a program stored in the memory 702 and executable on the processor 701; the processor 701 is used to read the program in the memory 702 to implement the steps in the above-described method for identifying key regions of a three-dimensional spatial network based on a graph neural network.

[0084] This application also provides a readable storage medium storing a program. When the program is executed by a processor, it implements the various processes of the above-described embodiment of the key region identification method for three-dimensional spatial networks based on graph neural networks, and achieves the same technical effect. To avoid repetition, it will not be described again here. The readable storage medium can be any available medium or data storage device that the processor can access, including but not limited to magnetic storage (such as floppy disks, hard disks, magnetic tapes, magneto-optical disks (MOs), etc.), optical storage (such as compact disks (CDs), digital video discs (DVDs), Blu-ray discs (BDs), high-definition universal discs (HVDs), etc.), and semiconductor storage (such as read-only memory (ROMs), erasable programmable read-only memory (EPROMs), electrically erasable programmable read-only memory (EEPROMs), non-volatile memory (NAND flash), solid-state drives (SSDs)).

[0085] It should be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes that element.

[0086] Through the above description of the embodiments, those skilled in the art can clearly understand that the methods of the above embodiments can be implemented by means of software plus necessary general-purpose hardware platforms. Of course, they can also be implemented by hardware, but in many cases the former is a better implementation method. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product is stored in a storage medium (such as ROM / RAM, disk, optical disk) and includes several instructions to cause a terminal (which may be a mobile phone, computer, server, air conditioner, or network device, etc.) to execute the methods described in the various embodiments of this application.

[0087] The embodiments of this application have been described above with reference to the accompanying drawings. However, this application is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other modifications under the guidance of this application without departing from its spirit, and all of these modifications are within the scope of protection of this application.

Claims

1. A method for identifying key regions in a three-dimensional spatial network based on a graph neural network, characterized in that, include: A drone communication network is constructed based on the distribution of drones in three-dimensional space. The drone communication network is a three-dimensional spatial network. The basic nodes in the drone communication network are used to represent the drones, and the edges between the basic nodes are used to represent the communication links between drones. The UAV communication network is divided into multiple non-overlapping regions to obtain a region map. Each region is used to represent a cube structure in the UAV communication network. The region nodes in the region map are used to represent the region, and the edges between the region nodes are used to represent the connection relationship between the regions. The initial feature representation of the region node is obtained based on the information of the base node corresponding to the region node; Based on the initial feature representation, the operation is performed on the region map. The layer neighborhood aggregation and representation update operations are used to obtain the aggregated feature representation of the region nodes; The aggregated feature representation is input into the prediction module for prediction to obtain a prediction score for each region. The prediction score is used to characterize the importance of the region in the UAV communication network.

2. The method for identifying key regions of a three-dimensional spatial network based on a graph neural network according to claim 1, characterized in that, The process of dividing the UAV communication network into multiple non-overlapping regions to obtain a region map includes: The original three-dimensional coordinate values ​​of the basic node in the three-dimensional space are standardized to obtain normalized coordinate values. Based on the normalized coordinate values, the UAV communication network is divided into multiple non-overlapping cubic regions to obtain the region map.

3. The method for identifying key regions of a three-dimensional spatial network based on a graph neural network according to claim 1, characterized in that, The connection relationship includes at least one of spatial adjacency relationship and entity interaction relationship. The spatial adjacency relationship is used to characterize that the cube structures corresponding to the two regions share a face, edge or vertex. The entity interaction relationship is used to characterize that there is an edge connection between the basic nodes contained in the two regions.

4. The method for identifying key regions of a three-dimensional spatial network based on a graph neural network according to claim 1, characterized in that, The step of obtaining the initial feature representation of the region node based on the information of the base node corresponding to the region node includes: The initial feature representation of the regional nodes is determined based on at least one of the regional degree centrality, regional webpage ranking, and regional collective influence. Wherein, the regional degree centrality is used to characterize the cumulative level of direct connectivity of the basic nodes contained in the region, the regional webpage ranking is used to characterize the relative importance of the basic nodes contained in the region in the overall connectivity of the UAV communication network, and the regional collective influence is used to characterize the degree of influence of the basic nodes contained in the region on the connectivity skeleton of the UAV communication network within a preset range.

5. The method for identifying key regions of a three-dimensional spatial network based on a graph neural network according to claim 4, characterized in that, Any region node in the region map Regional Degree Centrality Regional webpage sorting and regional collective influence They are respectively: ； ； ； in, Basic Node Degree centrality, Basic Node The degree, Let be the number of edges in the drone communication network. Basic Node Page ranking value Basic Node In radius The collective influence value.

6. The method for identifying key regions of a three-dimensional spatial network based on a graph neural network according to claim 1, characterized in that, The representation based on the initial features is executed on the region map. The layer neighborhood aggregation and representation update operation yields the aggregated feature representation of the region nodes, including: The region map is input map sampling and aggregation encoder, and then executed. The layer neighborhood aggregation and representation update operations yield the aggregated feature representation of the region nodes. It is a positive integer; Among them, the Layer neighborhood aggregation and representation update operations include: The neighboring nodes of the target node are in the th order. The feature representations of the layers are aggregated to obtain the target node at the 1st layer. The neighborhood aggregation representation of the layer indicates that the target node is any of the region nodes, and the neighbor nodes are the region nodes in the region graph that are connected to the target node. ; The target node is in the first The feature representation of the layer and the target node in the th layer After concatenating the neighborhood aggregation representations of the layers, the target node at the 1st rank is obtained through linear transformation and nonlinear activation function. The feature representation of the layer, the target node in the th layer The feature representation of a layer is the aggregated feature representation of the target node, and the feature representation of the target node in layer 0 is the initial feature representation of the target node.

7. The method for identifying key regions of a three-dimensional spatial network based on a graph neural network according to claim 1, characterized in that, After inputting the aggregated feature representation into the prediction module for prediction to obtain a prediction score for each region, the method further includes: A resource allocation strategy is formulated based on the predicted score of each of the regions. Based on the resource allocation strategy, communication resources are allocated to each of the regions.

8. A device for identifying key regions of a three-dimensional spatial network based on a graph neural network, characterized in that, include: A construction module is used to construct a UAV communication network based on the distribution of UAVs in three-dimensional space. The UAV communication network is a three-dimensional spatial network. The basic nodes in the UAV communication network are used to represent the UAVs, and the edges between the basic nodes are used to represent the communication links between the UAVs. The partitioning module is used to divide the UAV communication network into multiple non-overlapping regions to obtain a region map. Each region is used to represent a cube structure in the UAV communication network. The region nodes in the region map are used to represent the regions, and the edges between the region nodes are used to represent the connection relationships between the regions. The acquisition module is used to acquire the initial feature representation of the region node based on the information of the base node corresponding to the region node; An execution module is configured to perform operations on the region map based on the initial feature representation. The layer neighborhood aggregation and representation update operations are used to obtain the aggregated feature representation of the region nodes; The prediction module is used to input the aggregated feature representation into the prediction module for prediction, and obtain a prediction score for each region. The prediction score is used to characterize the importance of the region in the UAV communication network.

9. An electronic device, comprising: A memory, a processor, and a program stored in the memory and executable on the processor, characterized in that the processor is configured to read the program from the memory to implement the steps in the method for identifying key regions of a three-dimensional spatial network based on a graph neural network as described in any one of claims 1 to 7.

10. A readable storage medium for storing a program, characterized in that, When the program is executed by the processor, it implements the steps in the method for identifying key regions of a three-dimensional spatial network based on a graph neural network as described in any one of claims 1 to 7.

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